The Prisoners' Dilemma (Mackie's version):
Two soldiers (let's call them Amy and Bob) are on guard at separate posts. They both hear noises indicating that the enemy is coming. They each have to decide: stick to their post, or flee? If they both stick to their posts, they have a good chance of surviving. If they both flee, the enemy will overrun their position, and they might be captured or killed. If one runs and one stays, the one who stays will probably die, but the one who runs has a good chance of getting away while the other guard holds them off.
What should the guards do? Cooperate (i.e., stay) or defect?
We can analyze their options with the help of the following table:
The entries in the table are the preference Amy and Bob respectively assign to each outcome: (1,4) indicates this outcome is the best for Amy (1) and the worst for Bob (4).
If Amy doesn't know what Bob is going to do, she will reason like this: "Suppose Bob decides to defect. Then my choices are to cooperate and probably die (4), or defect (3) and run the risks of the enemy overrunning our position. So I should choose to defect.
Now suppose Bob decides to cooperate. If I cooperate too, then we have a good chance of surviving (2). But if I defect, I have an even better chance of surviving (1). So I should decide to defect."
Bob reasons the same way, of course, so both decide to defect. Both have chosen rationally, but the outcome is sub-optimal. From a global perspective, both of them cooperating is clearly preferable.
This simple example from game theory helps us understand how moral systems might have evolved. Individuals with a disposition to cooperate can end up with a better chance of surviving than individuals acting purely from their own self-interest. This is the hook that evolution can latch onto to promote cooperation.
A more detailed game theoretical analysis shows that when the situation is repeated many times - rather than the one-off situation described above - cooperation can actually be rationally justified.
And this is just the situation we find ourselves in. Every day, we make thousands of decisions whether to cooperate and do what morality dictates - keep that promise, pay for that coffee, obey that traffic signal - or to defect.
And most of us, most of the time, decide to cooperate. But is this rational behavior?